Hi,

     .

A = (10cm)(25cm) = 250cm^2

Question States***

A = (10cm + x)(25cm + x) = 500cm^2

x^2 + 35x - 500 = 0   (Tossing out the negative solution for unit measure)

 


 
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation  (in our case ) has the following solutons:

  

  

  

  For these solutions to exist, the discriminant  should not be a negative number.

  

  First, we need to compute the discriminant : .

  

  Discriminant d=3225 is greater than zero. That means that there are two solutions: .

  

    

    

    

    Quadratic expression  can be factored:

  

  Again, the answer is: 10.8945417290014, -45.8945417290014.
Here's your graph:



  

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
 the area is increased by the square of the increase in the dimensions.





this means that, if the dimensions are increased by a factor of 2, then the area is increased by a factor of 2^2 = 4.





working backward, if the area is increased by a factor of 4, then the dimensions are increased by a factor of sqrt(4) = 2.





in your problem, the area was increased by a factor of 2.





using the rule shown above, this means that the dimensions must be increased by a factor of sqrt(2).





let's see if this rule holds.





your original area is 10 * 25 = 250 square units.





you multiply the area by a factor of 2 which means your new area is 500 square units.





you need to multiply your dimensions by a factor of sqrt(2) if the rule holds.





you will get:





10*sqrt(2)*25*sqrt(2) = 10*25*sqrt(2)*sqrt(2)= 10*25*2 = 500.





the rule works.





your solution is that each dimension must be multiplied by a factor of sqrt(2).







 

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